3.1 statements and logical connectives · 2015-09-28 · 3.1 statements and logical connectives...
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3.1 Statements and Logical Connectives FILLED IN NOTES.notebook September 30, 2014
3.1 Statements and Logical Connectives
3.1 Statements and Logical Connectives FILLED IN NOTES.notebook September 30, 2014
HISTORYAristotle is called the father of logic. Logic from his time period is called Aristotelian logic and it has been taught/studied for over 2000 years.
Gottfried Wilhelm Liebniz is the father of symbolic logic which we will be studying in this class.
Charles Dodgson a.k.a. Lewis Carroll incorporated many ideas from logic into his famous book Alice's Adventures in Wonderland.
3.1 Statements and Logical Connectives FILLED IN NOTES.notebook September 30, 2014
Logic has been studied through the ages to exercise the mind's ability to reason. Understanding logic will enable you to think clearly, communicate effectively, make more convincing arguments, and develop patterns of reasoning that will help you in making decisions. It will also help you detect the fallacies in the reasoning or arguments of others such as advertisers and politicians.
3.1 Statements and Logical Connectives FILLED IN NOTES.notebook September 30, 2014
LOGIC AND THE ENGLISH LANGUAGE
Connectives the words and, or, if...then, both, etc. the words used to connect thoughts
Exclusive or when the exclusive or is used, one or the other of the events can take place, but not both
ex. You may have a cup of soup or a half sandwich with your salad.
Inclusive or when the inclusive or is used, one or the other, or both events can take place
ex. Your punishment is community service or a fine.
In this class the inclusive or is used unless stated otherwise.
3.1 Statements and Logical Connectives FILLED IN NOTES.notebook September 30, 2014
STATEMENTS AND LOGICAL CONNECTIVES
Statement A sentence that can be judged either true or false
Simple statement a sentence that conveys only one idea.
ex. The Brooklyn Bridge goes over San Francisco Bay
Compound Statement a sentence that conveys more than one idea whichare linked by connectives.
ex. I will go to the birthday party or I will send a present.
3.1 Statements and Logical Connectives FILLED IN NOTES.notebook September 30, 2014
QUANTIFIERS
Negation changing a statement to its opposite meaning
The negation of a true statement is always falseThe negation of a false statement is always true
Quantifiers words that describe how much or how manyex. all, none (or no), some
Form of statement From of negation
All are Some are not.
None are Some are.
Some are None are.
Some are not All are.
3.1 Statements and Logical Connectives FILLED IN NOTES.notebook September 30, 2014
SYMBOLIC LOGICEach idea is represented by a single letter, usually p, q, r, s, etc.
Not statements: ~p
And statements: these are conjucntions symbolized by p ^ q Or statements: these are disjunctions symbolized by p v q
Ifthen statements: these are conditional statements symbolized by p > q
If and only if statements: these are biconditional statements symbolized by p <> q
An idea that is a negation cannot be represented by a letter.
3.1 Statements and Logical Connectives FILLED IN NOTES.notebook September 30, 2014
Grouping: the simple statements on the same side of the comma are to be grouped together within parentheses.
GROUPING AND DOMINANCE OF CONNECTIVES
Table of Dominance:
Least Dominant Evaluate First
Most Dominant Evaluate Last
3.1 Statements and Logical Connectives FILLED IN NOTES.notebook September 30, 2014
Example 1: Write the statements in symbolic form. Identify which letter is used for which idea.
a) Some students are athletes
b) Some dogs are not great danes.
c) Maria will go to the circus or Maria will go to the zoo.
d)Dinner includes soup, and the salad or vegetable of the day
e)Joseph is making breakfast and Mike is not setting the table
f)If Jennifer goes to the library then Jennifer will study.
3.1 Statements and Logical Connectives FILLED IN NOTES.notebook September 30, 2014
Example 1 Continued:g) It is false that if June will go to the pool then she will swim.
h) Jorge will major in criminal science if and only if Jorge attends Georgetown.
i) If Jorge's major is criminal justice, then Jorge is not enrolled in calculus or Jorge's major is engineering.
j) You are late in paying your rent, or if you have damaged the apartment then you may be evicted.
k) It is false that the printer is working if and only if the ink cartridge is not correctly inserted.
l)John is neither handsome nor rich.
3.1 Statements and Logical Connectives FILLED IN NOTES.notebook September 30, 2014
Example 2: Write each symbolic statement in words. Letp: The sun is shining.q: We go to Six Flags.r: We ride roller coasters.
a) ( p v q) ^ ~r
b) ~p > (q v r)
c) (q <> p) ^ r
3.1 Statements and Logical Connectives FILLED IN NOTES.notebook September 30, 2014
Example 3: Add parentheses by using the dominance of connectives and the state if the statement is a negation, conjunction, disjunction, conditional, or biconditional.
a) ~p > q
b) ~ p ^ ~q
c) p v q > r
d) ~ p <> ~ q > r
e) ~[p ^ q <> p v r]